Nuprl Lemma : mFOL-proveable-formula-evidence
Main Lemma. See mFOL-proveable-evidence also.⋅
∀[fmla:mFOL()]. (mFOL-proveable-formula(fmla) 
⇒ mFOL-evidence(fmla))
Proof
Definitions occuring in Statement : 
mFOL-proveable-formula: mFOL-proveable-formula(fmla)
, 
mFOL-evidence: mFOL-evidence(fmla)
, 
mFOL: mFOL()
, 
uall: ∀[x:A]. B[x]
, 
implies: P 
⇒ Q
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
implies: P 
⇒ Q
, 
mFOL-proveable-formula: mFOL-proveable-formula(fmla)
, 
member: t ∈ T
, 
subtype_rel: A ⊆r B
, 
mFOL-sequent: mFOL-sequent()
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
uimplies: b supposing a
, 
all: ∀x:A. B[x]
, 
mFOL-evidence: mFOL-evidence(fmla)
, 
mFO-uniform-evidence: mFO-uniform-evidence(vs;fmla)
, 
prop: ℙ
, 
mFOL-sequent-evidence: mFOL-sequent-evidence(s)
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
rev_implies: P 
⇐ Q
, 
pi2: snd(t)
, 
pi1: fst(t)
, 
false: False
, 
mFOL-sequent-abstract: mFOL-sequent-abstract(s)
, 
FOSatWith: Dom,S,a |= fmla
, 
unit: Unit
, 
tuple-type: tuple-type(L)
, 
list_ind: list_ind, 
mFOL-hyps-meaning: mFOL-hyps-meaning(Dom;S;a;hyps)
, 
map: map(f;as)
, 
nil: []
, 
it: ⋅
Lemmas referenced : 
mFOL-proveable-evidence, 
nil_wf, 
subtype_rel_product, 
list_wf, 
mFOL_wf, 
subtype_rel_list, 
subtype_rel_self, 
FOAssignment_wf, 
mFOL-freevars_wf, 
FOStruct_wf, 
mFOL-proveable-formula_wf, 
subtype_rel_FOAssignment, 
mFOL-sequent-freevars_wf, 
mFOL-sequent-freevars-contained, 
l_contains_weakening, 
nil_member, 
l_member_wf, 
it_wf, 
equal-wf-base
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
lambdaFormation, 
sqequalHypSubstitution, 
cut, 
introduction, 
extract_by_obid, 
isectElimination, 
thin, 
independent_pairEquality, 
voidEquality, 
hypothesis, 
hypothesisEquality, 
applyEquality, 
sqequalRule, 
lambdaEquality, 
independent_isectElimination, 
voidElimination, 
because_Cache, 
independent_functionElimination, 
cumulativity, 
universeEquality, 
dependent_functionElimination, 
productElimination, 
independent_pairFormation, 
intEquality, 
baseClosed
Latex:
\mforall{}[fmla:mFOL()].  (mFOL-proveable-formula(fmla)  {}\mRightarrow{}  mFOL-evidence(fmla))
Date html generated:
2018_05_21-PM-10_39_56
Last ObjectModification:
2017_07_26-PM-06_42_14
Theory : minimal-first-order-logic
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