Nuprl Lemma : mset_for_inj_lemma
∀f,a,y,g,s:Top. (msFor{g} x ∈ mset_inj{s}(y) + a. f[x] ~ f[y] * (msFor{g} x ∈ a. f[x]))
Proof
Definitions occuring in Statement :
mset_for: mset_for,
mset_sum: a + b,
mset_inj: mset_inj{s}(x),
top: Top,
infix_ap: x f y,
so_apply: x[s],
all: ∀x:A. B[x],
sqequal: s ~ t,
grp_op: *
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
mset_for: mset_for,
mset_inj: mset_inj{s}(x),
mset_sum: a + b,
mk_mset: mk_mset(as),
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
istype-top,
list_ind_cons_lemma,
istype-void,
list_ind_nil_lemma,
mon_for_cons_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
hypothesis,
inhabitedIsType,
hypothesisEquality,
introduction,
extract_by_obid,
sqequalRule,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality_alt,
voidElimination
Latex:
\mforall{}f,a,y,g,s:Top. (msFor\{g\} x \mmember{} mset\_inj\{s\}(y) + a. f[x] \msim{} f[y] * (msFor\{g\} x \mmember{} a. f[x]))
Date html generated:
2019_10_16-PM-01_06_35
Last ObjectModification:
2018_10_08-PM-00_46_01
Theory : mset
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