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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