Nuprl Lemma : fan-iff-dfan-bool
Fan ⇐⇒ Fan
Proof
Definitions occuring in Statement :
fan: Fan,
dfan: Fan_d(T),
bool: 𝔹,
iff: P ⇐⇒ Q
Definitions unfolded in proof :
dfan: Fan_d(T),
fan: Fan,
ubar: ubar(T;X),
tbar: tbar(T;X),
dec-predicate: Decidable(X),
dbar: dbar(T;X),
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q,
cand: A c∧ B,
guard: {T}
Lemmas referenced :
and_wf,
dec-predicate_wf,
list_wf,
bool_wf,
tbar_wf,
all_wf,
ubar_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
independent_pairFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
lemma_by_obid,
isectElimination,
hypothesis,
hypothesisEquality,
functionEquality,
cumulativity,
universeEquality,
instantiate,
lambdaEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
Fan \mLeftarrow{}{}\mRightarrow{} Fan
Date html generated:
2016_05_14-PM-04_12_45
Last ObjectModification:
2015_12_26-PM-07_53_57
Theory : fan-theorem
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