Nuprl Lemma : fan_wf
Fan ∈ ℙ'
Proof
Definitions occuring in Statement :
fan: Fan,
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
fan: Fan,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
so_apply: x[s],
nat: ℕ,
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
all: ∀x:A. B[x],
int_seg: {i..j-}
Lemmas referenced :
all_wf,
list_wf,
bool_wf,
decidable_wf,
nat_wf,
exists_wf,
map_wf,
int_seg_wf,
subtype_rel_dep_function,
int_seg_subtype_nat,
false_wf,
subtype_rel_self,
upto_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesis,
applyEquality,
lambdaEquality,
cumulativity,
hypothesisEquality,
universeEquality,
because_Cache,
natural_numberEquality,
setElimination,
rename,
independent_isectElimination,
independent_pairFormation,
lambdaFormation
Latex:
Fan \mmember{} \mBbbP{}'
Date html generated:
2016_05_14-PM-04_12_28
Last ObjectModification:
2015_12_26-PM-07_54_12
Theory : fan-theorem
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