Nuprl Lemma : deq-mFO_wf
deq-mFO() ∈ EqDecider(mFOL())
Proof
Definitions occuring in Statement : 
deq-mFO: deq-mFO()
, 
mFOL: mFOL()
, 
deq: EqDecider(T)
, 
member: t ∈ T
Definitions unfolded in proof : 
deq: EqDecider(T)
, 
deq-mFO: deq-mFO()
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
rev_implies: P 
⇐ Q
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
uiff: uiff(P;Q)
, 
rev_uimplies: rev_uimplies(P;Q)
, 
uimplies: b supposing a
Lemmas referenced : 
eq_mFO_wf, 
mFOL_wf, 
equal_wf, 
assert_wf, 
all_wf, 
iff_wf, 
assert-eq_mFO
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
sqequalRule, 
dependent_set_memberEquality, 
lambdaEquality, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
lambdaFormation, 
independent_pairFormation, 
applyEquality, 
productElimination, 
independent_isectElimination
Latex:
deq-mFO()  \mmember{}  EqDecider(mFOL())
Date html generated:
2016_05_15-PM-10_14_34
Last ObjectModification:
2015_12_27-PM-06_32_54
Theory : minimal-first-order-logic
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