Nuprl Lemma : mFOL-subst_wf
∀[fmla:mFOL()]. ∀[nw,old:ℤ].  (fmla[nw/old] ∈ mFOL())
Proof
Definitions occuring in Statement : 
mFOL-subst: fmla[nw/old]
, 
mFOL: mFOL()
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
int: ℤ
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
mFOL-subst: fmla[nw/old]
, 
all: ∀x:A. B[x]
, 
subtype_rel: A ⊆r B
, 
and: P ∧ Q
, 
prop: ℙ
, 
uimplies: b supposing a
, 
squash: ↓T
, 
true: True
Lemmas referenced : 
mFOL-rename_wf, 
mFOL-rename-bound-to-avoid_wf, 
cons_wf, 
nil_wf, 
equal_wf, 
list_wf, 
mFOL-freevars_wf, 
length_wf, 
mFOL-abstract_wf, 
subtype_rel-equal, 
AbstractFOFormula_wf, 
l_disjoint_wf, 
mFOL-boundvars_wf, 
mFOL_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalRule, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
dependent_functionElimination, 
hypothesisEquality, 
intEquality, 
because_Cache, 
hypothesis, 
applyEquality, 
lambdaEquality, 
setElimination, 
rename, 
setEquality, 
productEquality, 
instantiate, 
cumulativity, 
universeEquality, 
applyLambdaEquality, 
independent_isectElimination, 
imageElimination, 
equalitySymmetry, 
natural_numberEquality, 
imageMemberEquality, 
baseClosed, 
axiomEquality, 
equalityTransitivity, 
isect_memberEquality
Latex:
\mforall{}[fmla:mFOL()].  \mforall{}[nw,old:\mBbbZ{}].    (fmla[nw/old]  \mmember{}  mFOL())
Date html generated:
2018_05_21-PM-10_24_16
Last ObjectModification:
2017_07_26-PM-06_38_27
Theory : minimal-first-order-logic
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