Nuprl Lemma : bool-deq_wf
BoolDeq ∈ EqDecider(𝔹)
Proof
Definitions occuring in Statement :
bool-deq: BoolDeq,
deq: EqDecider(T),
bool: 𝔹,
member: t ∈ T
Definitions unfolded in proof :
deq: EqDecider(T),
bool-deq: BoolDeq,
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,
uiff: uiff(P;Q),
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
eq_bool_wf,
bool_wf,
equal_wf,
assert_of_eq_bool,
assert_wf,
all_wf,
iff_wf
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,
because_Cache,
addLevel,
allFunctionality,
productElimination,
impliesFunctionality,
independent_isectElimination,
applyEquality
Latex:
BoolDeq \mmember{} EqDecider(\mBbbB{})
Date html generated:
2016_05_14-AM-06_07_14
Last ObjectModification:
2015_12_26-AM-11_46_12
Theory : equality!deciders
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